Annulus Area 886C75

1. **State the problem:** We need to find the exact area of the shaded annulus (ring) formed between two concentric circles with radii $22$ ft and $29$ ft. 2. **Formula used:** The area of an annulus is given by the difference of the areas of the outer and inner circles: $$\text{Area} = \pi R^2 - \pi r^2 = \pi (R^2 - r^2)$$ where $R$ is the outer radius and $r$ is the inner radius. 3. **Substitute the values:** $$\text{Area} = \pi (29^2 - 22^2)$$ 4. **Calculate the squares:** $$29^2 = 841$$ $$22^2 = 484$$ 5. **Subtract the squares:** $$841 - 484 = 357$$ 6. **Write the area expression:** $$\text{Area} = \pi \times 357 = 357\pi$$ 7. **Final answer:** The exact area of the shaded region is $$\boxed{357\pi \text{ ft}^2}$$